cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A068647 Primes in which a string of 6's is sandwiched between two 1's.

Original entry on oeis.org

11, 16661, 1666666666661, 16666666666666661, 1666666666666666661, 1666666666666666666666666666666666661, 16666666666666666666666666666666666666666666666666661
Offset: 1

Views

Author

Amarnath Murthy, Feb 28 2002

Keywords

Comments

The next term -- a(8) -- has 73 digits. - Harvey P. Dale, Jun 18 2021

Examples

			11 is also a member in which a string of 0 6's is there between two one's.
		

Crossrefs

Programs

  • Mathematica
    Select[Table[10*FromDigits[PadRight[{1},n,6]]+1,{n,60}],PrimeQ] (* Harvey P. Dale, Jun 18 2021 *)

Extensions

More terms from Sascha Kurz, Mar 19 2002
Edited by Ray Chandler, Nov 04 2014

A156166 Numbers k > 0 such that (10^(k+2) + 666)*10^k + 1 is prime.

Original entry on oeis.org

1, 14, 43, 507, 609, 2473, 2624, 28292, 181299
Offset: 1

Views

Author

M. F. Hasler, Feb 10 2009

Keywords

Comments

Or, indices of primes in the sequence 16661, 1066601, 100666001, 10006660001,... Ondrejka calls these "beastly palindromic primes".
In popular culture: the number generated by a(2), 1000000000000066600000000000001, also known as Belphegor's Prime, was used as a plot device in Episode "Just a Regular Irregular" of the "Elementary" TV series (first aired Nov/13/2014). - Serge Batalov, Nov 15 2014

Crossrefs

Cf. A082700 and search results for 16661.
Cf. A232448 (a(n) - 1).

Programs

  • Magma
    [n: n in [1..500] | IsPrime((10^(n+2)+666)*10^n+1)]; // Vincenzo Librandi, Nov 15 2014
  • Maple
    A156166:=n->`if`(isprime((10^(n+2)+666)*10^n+1), n, NULL): seq(A156166(n), n=1..10^3); # Wesley Ivan Hurt, Nov 16 2014
  • Mathematica
    Select[Range[10^3], PrimeQ[(10^(# + 2) + 666)*10^# + 1] &] (* Arkadiusz Wesolowski, Sep 08 2011 *)
  • PARI
    for( n=1,9999, ispseudoprime((10^(n+2)+666)*10^n+1) & print1(n","))
    

Formula

a(n) = A232448(n) + 1.

Extensions

a(8) = 28292 (discovered on Jan 05 2004, by Daniel Heuer), Arkadiusz Wesolowski, Mar 16 2011
a(9) = 181299 from Serge Batalov, Nov 15 2014

A056247 Indices of primes in sequence defined by A(0) = 11, A(n) = 10*A(n-1) + 51 for n > 0.

Original entry on oeis.org

0, 3, 11, 15, 17, 35, 51, 71, 99, 6231, 24027, 40221, 66393
Offset: 1

Views

Author

Robert G. Wilson v, Aug 18 2000

Keywords

Comments

Numbers n such that (150*10^n - 51)/9 is prime.
Numbers n such that digit 1 followed by n >= 0 occurrences of digit 6 followed by digit 1 is prime.
Numbers corresponding to terms <= 99 are certified primes.

Examples

			16661 is prime, hence 3 is a term.
		

References

  • Klaus Brockhaus and Walter Oberschelp, Zahlenfolgen mit homogenem Ziffernkern, MNU 59/8 (2006), pp. 462-467.

Crossrefs

Programs

  • Mathematica
    Select[Range[0, 2000], PrimeQ[(150 10^# - 51) / 9] &] (* Vincenzo Librandi, Nov 03 2014 *)
  • PARI
    a=11;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a+51)
    
  • PARI
    for(n=0,1500,if(isprime((150*10^n-51)/9),print1(n,",")))

Formula

a(n) = A082700(n-1) - 2 for n > 1.

Extensions

Additional comments from Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 28 2004
Edited by N. J. A. Sloane, Jun 15 2007
More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008
Added one more term from the PDP table and a link, by Patrick De Geest, Nov 02 2014
Edited by Ray Chandler, Nov 04 2014
Showing 1-3 of 3 results.